How to move the keyframes for specified shape keys with Python
This script gives you the ability to list the names of the shapekeys you want to shift, then move only them by the keyframeInterval value you want.

It uses a regular expression pattern to match the shapekey name to the fcurve data path string.

import bpy, re

o = bpy.context.object

sk  = o.data.shape_keys
act = sk.animation_data.action if sk and sk.animation_data else None

keyframeInterval = 10 # Number of frames to move shape keys
keysToShift = ['Key 2', 'Key 3'] # List of shape keys you want to move (names)

# Regular expression pattern to find key in fcurve data path.
# Example: 'key_blocks["Key 1"].value'
pat = '^key_blocks\["(.+)"\]\.value$'

if act:
    for fc in act.fcurves:
        m = re.match( pat, fc.data_path )
        if m and m.groups() and m.groups()[0] in keysToShift:
            for kf in fc.keyframe_points:
                kf.co.x += keyframeInterval